Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Weekly Problem 36 - 2010

Stage: 2 and 3 Short Challenge Level:

One way to proceed is to regard the pattern as four arms, each two
squares wide, with four corner pieces of three squares each. So for
the $n_{th}$ pattern, we have $4 \times 2 \times n + 4 \times 3 =
8n +12$. For $n=10$, we need $8 \times 10 +12$, i.e. $92$
squares.

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